% Matlab code to estimate a mixed logit model with maximum simulated likelihood
% Written by Kenneth Train, first version July 19, 2006, 
% Mixed logit computation - Random coefficients distributed Restricted
% Restricted triangular distribution
% Modified by Gianmarco Leon on June 20th, 2016
% for Leon and Miguel (2016) Transportation choices and the Value of
% Statistical Life, AEJ Applied

clear all

% Declare GLOBAL variables
% GLOBAL variables are all in caps
% DO NOT CHANGE ANY OF THESE 'global' STATEMENTS
global NP NCS NROWS
global IDV NV NAMES B W
global IDF NF NAMESF F
global DRAWTYPE NDRAWS SEED1 SAVEDR PUTDR
global WANTWGT IDWGT WGT
global NALTMAX NCSMAX
global X XF S DR
global XMAT
global NMEM NTAKES NPARAM
global MDR
global A NA

% OUTPUT FILE
% Put the name you want for your output file (including full path if not the current 
% working directory) after words "delete" and "diary".
% The 'diary off' and 'delete filename' commands close and delete the previous version 
% of the file created during your current matlab session or in any previous sessions. 
% If you want to append the new output to the old output, then 
% put % in front of the 'diary off' and 'delete filename' commands (or erase them).

diary mixed_logit_RestTriang_100_draws_20160620.out

% TITLE
% Put a title for the run in the quotes below, to be printed at the top of the output file.
disp 'Mixed logit with 100 MLHS draws: Restricted Triangular Distribution for Random Coefficients'

% DATA: Here we use a different dataset for each regression as indicated
% below. For each regression, un-comment the relevant sample to be used

% Table 5: Value of Statistical Life estimates in different sub samples and
% with alternative specifications

% Row (8) Full Sample, with weather controls interacted w/ risk and cost
sample2012all
% Row (9) Africans, with weather controls interacted w/ risk and cost
%sample2012af 
% Row (10) Non-Africans, with weather controls interacted w/ risk and cost
%sample2012noaf 

% Load and/or create XMAT, a matrix that contains the data.
%
% XMAT must contain one row of data for each alternative in each choice situation for each person.
% The rows are grouped by person, and by choice situations faced by each person.
% The number of rows in XMAT must be NROWS, specified above.
% The columns in XMAT are variable that describe the alternative.
% 
% The *first* column of XMAT identifies the person who faced this alternative. 
% The people must be numbered sequentially from 1 to NP, in ascending order.
% All alternatives for a given person must be grouped together.
% The *second* column of XMAT identifies the choice situation. The choice
% situations must be numbered sequentially from 1 to NCS.
% All alternatives for a given choice situation must be grouped together.
% The *third* column of XMAT identifies the chosen alternatives (1 for
% chosen, 0 for not). One and only one alternative must be chosen for each
% choice situation.
% The remaining columns of XMAT can be any variables.

% To help you keep up with the variables, list the variables in XMAT here.
% Start each line with % so that matlab sees that it is a comment rather than a command.
% The variables in XMAT are:
% 1. Person number (1-NP)            MUST BE THIS. DO NOT CHANGE.
% 2. Choice situation number (1-NCS) MUST BE THIS. DO NOT CHANGE.
% 3. Chosen alternative (1/0)        MUST BE THIS. DO NOT CHANGE.
% 4. Mode of transport 
% 5. Observed probability of completing the trip
% 6. Transportation cost
% 7. Weight
% 8. Seats
% 9. Noise
% 10. Crowdedness
% 11. Convenient location
% 12. Quality of the clientele

% Interactions between weather variables and risk and cost: 43-54
% interactions between calendar month and mode: 55-87

% Weather variables interacted with risk and cost


% MODEL SPECIFICATION

% RANDOM COEFFICIENTS
% List the variables in XMAT that enter the model with random coefficients and
% give the distribution for the coefficient of each variable.
% IDV contains one row for each random coefficient and two columns.
% The *first* column gives the number of a variable in XMAT that has a random coefficient, 
% and the *second* column specifies the distribution of the coefficient for that variable.
% The distributions can be 
% 1. normal: N(b,w^2) where mean b and standard deviation w are estimated.
% 2. lognormal: coefficient is exp(beta) where beta~N(b,w^2) with b and w estimated
% 3. truncated normal, with the share below zero massed at zero: max(0,beta) where 
%                      beta~N(b,w^2) with b and w estimated.
% 4. S_B: exp(beta)/(1+exp(beta))  where beta~N(b,w^2) with b and w estimated.
% 5. normal with zero mean (for error components): N(0,w^2) where w is estimated.
% 6. triangular: b+w*t where t is triangular between -1 and 1 and mean b and spread w are estimated.
% 7.truncated normal, with the share below zero massed at a small number greater than zero: max(10^(-20),beta) where 
%                      beta~N(b,w^2) with b and w estimated. see trans.m
% 8. S_B with free K: restrict coefficient to [0 K]
% 9. restricted triangular: a+a*t where t is triangular between -1 and 1
% and mean a and spread a are estimated.
% If no random coefficients, put IDV=[];
% Notes:
% The lognormal, truncated normal, and S_B distributions give positive
% coefficients only. If you want a variable to have only negative coefficients, 
% create the negative of the variable (in the specification of XMAT above).
% The S_B distribution gives coefficients between 0 and 1. If you want
% coefficients to be between 0 and k, then multiply the variable by k (in the specification 
% of XMAT above), since b*k*x for b~(0-1) is the same as b*x for b~(0-k).
% If no random coefficients, put IDV=[];
 
IDV=[ 5 9; ...
    6 9];
  
NV=size(IDV,1); %Number of random coefficients. Do not change this line.

%%%%%%%%%%%%%Key line in triangular case: this is one change I made from Prof Train's code%%%%%%%%%%%%%%%%%%%%%%

NA=sum(IDV(:,2) == 9);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 

% Give a name to each of the explanatory variables in IDV. They can 
% have up to ten characters including spaces. Put the names in single quotes and separate 
% the quotes with semicolons. If IDV=[], then set NAMES=[];

NAMES={'ProbComp';'TranspCost'}; 

% Starting values
% Specify the starting values for b and w for each random coeffient.
% B contains the first parameter, b, for each random coefficient.  
% It is a column vector with the same length as IDV. For distribution 5 (normal with zero mean),
% put 0 for the starting value for the mean. The code will keep it at 0.
% W contains the second parameter, w, for each random coefficient.
% It is a column vector with the same length as IDV.
% Put semicolons between the elements of B and W (so they will be column vectors).


%%%%%%%%%%%%%Key line in triangular case: this is one change I made from Prof Train's code%%%%%%%%%%%%%%%%%%%%%%

A=[1;0.1];
B=[A];
W=[A];


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
% FIXED COEFFICIENTS
% List the variables in XMAT that enter with fixed coefficients.
% Put semicolons between the numbers.
% If no fixed coefficients, put IDF=[];

IDF=[8;9;10;11;12;43;44;45;46;49;50;51;52;53;54]; % including interactions between weather and risk and cost

NF=size(IDF,1); %Number of fixed coefficients. Do not change this line.

% Give a name to each of the variables in IDF.
NAMESF={'Seats'; 'Noise'; 'Crowdedness' ; 'ConvLoc' ; 'Clientele';'Temp1';'Temp2';'Dew1';'Dew2';'Sea1';'Sea2';'Visib1';'Visib2';'Wind1';'Wind2'};

% Starting values.
% Specify the starting values for the fixed coefficients F.
% F must have the same length as IDF and have one column.
% Put semicolons between the elements (so F will be a column vector.)
F=[0;0;0;0;0;0;0;0;0;0;0;0;0;0;0];


% Type of draws to use in simulation
% 1=pseudo-random draws
% 2=standard Halton draws
% 3=shifted and shuffled Halton draws
% 4=modified Latin hypercube sampling, shifted and shuffled 
% 5=create your own draws or load draws from file
DRAWTYPE=4;

% Number of draws from to use per person in simulation.
NDRAWS=500;

% Set seed for the random number generator.
SEED1 = 14239; 

% If DRAWTYPE=5, then create or load the draws here.
% Create or load a data array, called DR, with dimensions NV x NP x NDRAWS.
% where element DR(i,j,k) is the k-th draw of random coefficient i for person j 
% Put your statements between "if DRAWTYPE==5" and "end".
% 
% If you created DR in a previous matlab session and saved it
% with "save mydraws DR" then put "load('mydraws.mat')" here. The structure
% mydraws will contain the array DR.
% Note: If you want to use the draws that were saved to PUTDR below in a 
% previous run, see the ReadMe.txt file for instructions.

if DRAWTYPE==5
   load('mydraws.mat');
end


% Memory use
% Give the number of draws that you want held in memory at one time.
% This number must be evenly divisible into the number of draws.
% That is NDRAWS./NMEM must be a positive integer.
% To hold all draws in memory at once, set NMEM=NDRAWS.
% A larger value of NMEM requires fewer reads from disc but 
% uses more memory which can slow-down the calculations and increases 
% the chance of running out of memory.
% If DRAWTYPE=5, then you must set NMEM=NDRAWS
NMEM=100;

% If all the draws are NOT held in memory at one time (that is, if NMEM<NDRAWS), 
% then give the filename (including full path if not in the working directory)
% that you want the draws to be temporarily saved to while the code is running.
% If all draws are held in memory at one time (that is, if NMEM=NDRAWS),
% then this file will not be created. So, if NMEM=NDRAWS, you can set PUTDR=''; 
% or give a file name, whichever you find more convenient, since the name won't be used.
PUTDR='draws';

% WEIGHTS. 
% Do you want to apply weights to the people? 
% Set WANTWGT=1 if you want to apply weights; otherwise set WANTWGT=0;
WANTWGT=1;

% If WANTWGT=1, identify the variable in XMAT that contains the weights.
% This variable can vary over people but must be the same for all rows of
% data for each person. Weights cannot vary over choice situations for
% each person or over alternatives for each choice situation -- only over people.
% The code normalizes the weights such that the sum 
% of weights over people is to equal NP (to assure that standard errors 
% are correctly calculated.) If WANTWGT=0, set IDWGT=[];
IDWGT=[7];

% OPTIMIZATION 
% Maximum number of iterations for the optimization routine.
% The code will abort after ITERMAX iterations, even if convergence has
% not been achieved. The default is 400, which is used when MAXITERS=[];
MAXITERS=[];

% Convergence criterion based on the maximum change in parameters that is considered
% to represent convergence. If all the parameters change by less than PARAMTOL 
% from one iteration to the next, then the code considers convergence to have been
% achieved. The default is 0.000001, which is used when PARAMTOL=[];
PARAMTOL=0.000001;

% Convergence criterion based on change in the log-likelihood that is
% considered to represent convergence. If the log-likelihood value changes
% less than LLTOL from one iteration to the next, then the optimization routine
% considers convergence to have been achieved. The default is 0.000001,
% which is used when LLTOL=[];
LLTOL=[];

%Do not change the next line. It runs the model.
doit

%Calculate individual level parameters.
COEFS=condmn(paramhat);

save COEFS.mat COEFS;

VSL=-COEFS(1,:)./COEFS(2,:);

% graph distribution of VSL
hist(VSL,100)

% Save VSL statistics
WTP=zeros(4,1);
    WTP(1,1)=mean(VSL);
    WTP(2,1)=median(VSL);
    WTP(3,1)=prctile(VSL,2.5);
    WTP(4,1)=prctile(VSL,97.5);

disp 'Number of travelers'
    NP(1,1)
disp 'Number of trips'
    NCS(1,1)
disp 'Log likelihood'
    fval(1,1)*(-1)
    
% Display VSL: Mean, Median, and 95% CI
disp 'Mean VSL'
WTP(1,1)
disp 'Lower CI'
WTP(3,1)
disp 'Upper CI'
WTP(4,1)

% Save the text file with the VSL estimates
    dlmwrite('VSL_est_all.txt',VSL)

    